ln(x+2)=ln(5-x)

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Solution for ln(x+2)=ln(5-x) equation: 


Simplifying
ln(x + 2) = ln(5 + -1x)

Reorder the terms:
ln(2 + x) = ln(5 + -1x)
(2 * ln + x * ln) = ln(5 + -1x)
(2ln + lnx) = ln(5 + -1x)
2ln + lnx = (5 * ln + -1x * ln)
2ln + lnx = (5ln + -1lnx)

Solving
2ln + lnx = 5ln + -1lnx

Solving for variable 'l'.

Move all terms containing l to the left, all other terms to the right.

Add '-5ln' to each side of the equation.
2ln + -5ln + lnx = 5ln + -5ln + -1lnx

Combine like terms: 2ln + -5ln = -3ln
-3ln + lnx = 5ln + -5ln + -1lnx

Combine like terms: 5ln + -5ln = 0
-3ln + lnx = 0 + -1lnx
-3ln + lnx = -1lnx

Add 'lnx' to each side of the equation.
-3ln + lnx + lnx = -1lnx + lnx

Combine like terms: lnx + lnx = 2lnx
-3ln + 2lnx = -1lnx + lnx

Combine like terms: -1lnx + lnx = 0
-3ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-3 + 2x) = 0


Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve:

Simplifying
ln = 0

Solving
ln = 0

Move all terms containing l to the left, all other terms to the right.

Simplifying
ln = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-3 + 2x)' equal to zero and attempt to solve:

Simplifying
-3 + 2x = 0

Solving
-3 + 2x = 0

Move all terms containing l to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + 2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2x = 0 + 3
2x = 0 + 3

Combine like terms: 0 + 3 = 3
2x = 3

Add '-2x' to each side of the equation.
2x + -2x = 3 + -2x

Combine like terms: 2x + -2x = 0
0 = 3 + -2x

Simplifying
0 = 3 + -2x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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